In the pair of equations a 1 x - b 1 y - c 1-0 and a 2 x - b 2 y - c 2-0a 1- a 2- b 1- b 2- c 1- c 2Which of the statements is-are correct-A- This is an inconsistent pair of linear equations-B- There exists infinitely many solutions-C- The lines representing these equations are parallel-D- There exists only one solution-

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Inconsistent Pair of Linear Equations

In the pair o...

Question

In the pair of equations
$a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ ,

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Which of the statements is/are correct?

This is an inconsistent pair of linear equations.

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There exists infinitely many solutions.

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The lines representing these equations are parallel.

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There exists only one solution.

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Solution

The correct options are
A This is an inconsistent pair of linear equations.
C The lines representing these equations are parallel.
In the pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ ,

if $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ , then the lines representing these equations are parallel.

Hence, there will be no solution and the pair of equations will be inconsistent.

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Similar questions

If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ in the system of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$

S1 : The following is condition for inconsistent equations

S2 : There exists infinitely many solutions

S3 : The equations satisfying the condition are parallel

Which of the following statements are true ?

State whether the given statement is true or false:

A pair of linear equations is given by

a_{1} x + b_{1} y + c_{1} = 0

and

a_{2} x + b_{2} y + c_{2} = 0

and

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

In this case, the pair of linear equations is inconsistent.

State true\false:

A pair of linear equations is given by

a_{1} x + b_{1} y + c_{1} = 0

and

a_{2} x + b_{2} y + c_{2} = 0

and

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}

In this case, the pair of linear equations is consistent.

Parallel lines are obtained for the pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ if

Q. In the pair of equations

a_{1} x + b_{1} y + c_{1} = 0

and

a_{2} x + b_{2} y + c_{2} = 0

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

Which of the statements is/are correct?

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In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0, a1a2=b1b2≠c1c2 Which of the statements is/are correct?

In the pair of equations
$a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ ,

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Which of the statements is/are correct?